Counterfeit Uno fails to respond via USBasp (signature 0x000000)

I happen to have a spare counterfeit Uno that I previously assumed unusable, since I had no means of reprogramming the firmware. However, I have recently obtained a USBasp and used it to re-burn the bootloader onto a MEGA2560 based board. Upon attempting to do the same for the Uno (with the respective board selected), it failed to respond, and upon forcing the upload in the command line (avrdude), the board would have a signature of 0x000000. This same signature would remain when using avrdude to check its status, and while I was able to restore the USB-to-serial connection by “burning” the bootloader, it still does not accept sketches.

Since this is one of the cheaper counterfeits from China, I wouldn’t be too surprised if the hardware actually failed, but before I throw it into the salvage heap I want to be sure that it is truly unrecoverable. After all, avrdude is able to show the table with the different types of storage and the details of their capacities, so there is some life in this board.

It may also be helpful to mention that this board was working about a year ago, while running a special firmware for a 3D scanner. One day it just stopped working, and after my attempts to upload a new sketch it refused to connect via USB.